**THE**

**BINARY NUMBER SYSTEM**

In the binary number system, 0 and 1 are the basic elements. Since there are only two digits in this scheme, we say that its radix is 2. The entire number system is built upon based on these two numbers. We call 0 and 1 as binary digits or

*bits*when they are used in the binary number system. 0 and 1, as stated above, can be used to represent any number in binary system. For example, (1101)_{2}represents a binary number, where the digits 1, 1, 0, and 1, represent coefficients of appropriate powers of 2. Thus For example, 1101 is a short form of writing, whose expansion is: (1101)

_{2}= (1*2^{3}) + (1*2^{2}) + (0*2^{1}) + (1*2^{0})Decimal equivalent of 1101)

_{2 }can be obtained by converting the powers of 2 to their respective decimal values. Thus(1101)

_{2}= (1*8) + (1*4) + (0*2) + 1 = 8 + 4+ 1 = (13)_{10}The procedure given above can be used to convert any binary number into its corresponding decimal number.